Nuclear magnetic resonance (NMR) is used as a tool in a number of different technology areas to investigate different types of mediums. NMR can occur when the medium is subjected to a static magnetic field, B0, and to an oscillating magnetic field, B1. When subjected to an applied static magnetic field, polarization of nuclear magnetic spins of the medium occurs based on spin number of the medium and magnetic field strength. Applying an electromagnetic field to the medium in the static magnetic field can perturb the polarization established by the static magnetic field. In optimal measurements, the static magnetic field and the perturbing field are perpendicular to each other. Collected responses received from the medium related to the total magnetization of nuclear spins in the medium, in response to these applied fields, can be used to investigate properties of the medium, and may provide imaging of the medium. It is noted that magnetization is proportional to polarization.
Nuclear magnetic resonance measurements are created by the oscillation of excited nuclear magnetic spins in the transverse plane, that is, the direction perpendicular to the magnetic field. This oscillation eventually dies out and the equilibrium magnetization returns. The return process is referred to as longitudinal relaxation. The time constant, T1, for nuclei to return to their equilibrium magnetization, Mo, is called the longitudinal relaxation time or the spin lattice relaxation time. The magnetization dephasing, that is losing coherence, along the transverse plane is given by the time constant T2 and is called the spin-spin relaxation time. The loss of phase coherence can be caused by several factors including interactions between spins, electrons, or magnetic gradients.
A widely used NMR measurement technique, designed by Carr, Purcell, Meiboom, and Gill and, hence, referred to as CPMG, uses a sequence of radio frequency pulses to produce spin echoes and counteract dephasing of the magnetization in the medium investigated. In the CPMG sequence, an initial pulse, commonly a 90° pulse, can be applied to tip the polarization into a plane perpendicular to the static magnetic field. To counter dephasing due to magnetic inhomogeneities, another pulse, a recovery pulse, commonly a 180° or other angle tipping pulse, is applied to return to phase, which produces a signal called an echo from the medium. Yet, after each return to phase, dephasing begins and another recovery pulse is applied for rephasing. Rephasing or refocusing is repeated many times in the CPMG sequence, followed by measuring each echo. The echo magnitude decreases with time due to a number of irreversible relaxation mechanisms. The CPMG sequence can have any number of echoes, where the time between each echo can be relatively short, for example, of the order of 0.5 ms or less or as long as 12 ms is used.
NMR logging tools have long proven their value to formation evaluation. Petrophysical information can be derived from NMR measurements, such as, but not limited to petrophysical properties of fluid containing porous media. Various properties that can be measured using an NMR logging tool include pore size, porosity, surface-to-volume ratio, formation permeability, and capillary pressure. These properties are determined from inversion of data. Recently, new drilling tools have added low-gradient magnet configurations to help reduce the effects of axis motion. The primary challenge associated with using low-gradient tools is the requirement of one preferred sensitive volume to be tracked over temperature. The secondary challenge is that the sensitive volume associated with low-gradient tools provides a vertically short sensitive volume. As a result, the tools are more sensitive to vertical motion, and thus to rate of penetration (ROP) or pulling speed, opposed to high-gradient configuration tools, particularly for T1 logging. Not only is porosity affected, but the T1 spectrum can also be distorted. Having a more reliable inversion may provide more precision in the evaluation of NMR data to generate correct porosity, T2 spectra, T1 spectra, diffusion spectra, and other parameters.